2. Research Topics

Digital Objects: Encoding and Enumeration Problems

The problem of encoding of digital objects (object which can be represented on the square integer grid in arbitrary dimensions) is mathematical in its nature, but the results have impact to several areas of computer science (e.g. neural networks theory or information theory). The encoding problem can be seen as the task of finding convenient labels for digital objects which should enable a fast comparison among the digital objects. Encoding by discrete moments is shown to be an efficient approach. To provide an efficient coding, one needs to balance the size and number of moments to achieve low storage and computation complexity. Enumerations problem is strictly related to the performance analysis of the established encoding schemes.

Shape Based Object Classification, Recognition and Identification

Image technologies have developed rapidly. A huge amount of images and images related data are available in different domains: medicine, biology, industry, geology, astronomy, crime prevention, security, etc. Different objects appear on images and they should be recognised, classified, or identified. Working in object space, i.e. comparing object pairwise is shown to be inaccurate and computationally expensive. A better idea is to map objects of interest onto a set of numbers (a vector in d-dimensional space) and then perform searching in this space. For such mapping we need some object characteristic which can be reasonably easily and efficiently quantified by numbers -- e.g. colour. The shape is another object characteristic, which allows a spectrum of numerical characterizations with a high discrimination capacity. There is a spectrum of applications, from biology to astronomy.

Multi-component Shape Approach in Computer Vision

Multi-component shape approach is introduced recently in computer vision and image processing tasks. Namely, very often it is better to consider a group of objects as a single multi-component object (fish shoal, vehicles on a road, etc.). Also, sometimes is more convenient to treat a single object, as a multi-component one, consisting of naturally defined components (e.g. cellular materials like bones, tissues, words or signatures decomposed onto characters, etc.). Another possibility is to consider an appearance of the same object in a frame sequence as a multi-component object.

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